| Title:
|
On the Borel-Cantelli Lemma and moments (English) |
| Author:
|
Amghibech, S. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
47 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
669-679 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present some extensions of the Borel-Cantelli Lemma in terms of moments. Our result can be viewed as a new improvement to the Borel-Cantelli Lemma. Our proofs are based on the expansion of moments of some partial sums by using Stirling numbers. We also give a comment concerning the results of Petrov V.V., {\it A generalization of the Borel-Cantelli Lemma\/}, Statist. Probab. Lett. {\bf 67} (2004), no. 3, 233--239. (English) |
| Keyword:
|
Borel-Cantelli Lemma |
| Keyword:
|
Stirling numbers |
| MSC:
|
05A18 |
| MSC:
|
60A10 |
| MSC:
|
60F15 |
| idZBL:
|
Zbl 1150.60305 |
| idMR:
|
MR2337421 |
| . |
| Date available:
|
2009-05-05T17:00:29Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119627 |
| . |
| Reference:
|
[1] Chung K.L., Erdös P.: On the application of the Borel-Cantelli Lemma.Trans. Amer. Math. Soc. 72 (1952), 1 179-186. MR 0045327 |
| Reference:
|
[2] Erdös P., Rényi A.: On Cantor's series with convergent $\Sigma 1/q_n$.Ann. Univ. Sci. Budapest Sect. Math. 2 (1959), 93-109. MR 0126414 |
| Reference:
|
[3] Kochen S.P., Stone C.J.: A note on the Borel-Cantelli Lemma.Illinois J. Math. 8 (1964), 248-251. Zbl 0139.35401, MR 0161355 |
| Reference:
|
[4] Lamperti J.: Wiener's test and Markov chains.J. Math. Anal. Appl. 6 (1963), 58-66. Zbl 0238.60044, MR 0143258 |
| Reference:
|
[5] Ortega J., Wschebor M.: On the sequence of partial maxima of some random sequences.Stochastic Process. Appl. 16 (1983), 85-98. MR 0723645 |
| Reference:
|
[6] Petrov V.V.: A note on the Borel-Cantelli Lemma.Statist. Probab. Lett. 58 (2002), 3 283-286. Zbl 1017.60004, MR 1921874 |
| Reference:
|
[7] Petrov V.V.: A generalization of the Borel-Cantelli Lemma.Statist. Probab. Lett. 67 (2004), 3 233-239. Zbl 1101.60300, MR 2053525 |
| Reference:
|
[8] Rényi A.: Probability Theory.North-Holland Series in Applied Mathematics and Mechanics, vol. 10, North-Holland, Amsterdam-London, 1970; German version 1962, French version 1966, new Hungarian edition 1965. MR 0315747 |
| Reference:
|
[9] Spitzer F.: Principles of Random Walk.2nd edition, Springer, New York-Heidelberg, 1976. Zbl 0979.60002, MR 0388547 |
| Reference:
|
[10] Van Lint J.H., Wilson R.M.: A Course in Combinatorics.2nd ed., Cambridge University Press, Cambridge, 2001. Zbl 0980.05001, MR 1871828 |
| . |
